Question: Simplify; express your answer in exponential form. Assume $r\neq 0, y\neq 0$. $\dfrac{{(r^{-5}y^{5})^{-4}}}{{(ry^{2})^{2}}}$
Explanation: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${(r^{-5}y^{5})^{-4} = (r^{-5})^{-4}(y^{5})^{-4}}$ On the left, we have ${r^{-5}}$ to the exponent ${-4}$ . Now ${-5 \times -4 = 20}$ , so ${(r^{-5})^{-4} = r^{20}}$ Apply the ideas above to simplify the equation. $\dfrac{{(r^{-5}y^{5})^{-4}}}{{(ry^{2})^{2}}} = \dfrac{{r^{20}y^{-20}}}{{r^{2}y^{4}}}$ Break up the equation by variable and simplify. $\dfrac{{r^{20}y^{-20}}}{{r^{2}y^{4}}} = \dfrac{{r^{20}}}{{r^{2}}} \cdot \dfrac{{y^{-20}}}{{y^{4}}} = r^{{20} - {2}} \cdot y^{{-20} - {4}} = r^{18}y^{-24}$